Residually finite properties of groups / Muhammad Sufi Mohd Asri
In this thesis, we shall study two stronger forms of residual finiteness, namely cyclic subgroup separability and weak potency in various generalized free products and HNN extensions. Among our results, we shall show that the generalized free products and HNN extensions where the amalgamated or a...
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| Format: | Thesis |
| Published: |
2018
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| Online Access: | http://studentsrepo.um.edu.my/10107/1/Muhammad_Sufi_Mohd_Asri.pdf http://studentsrepo.um.edu.my/10107/2/Muhammad_Sufi_Mohd_Asri_%E2%80%93_Dissertation.pdf http://studentsrepo.um.edu.my/10107/ |
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| Summary: | In this thesis, we shall study two stronger forms of residual finiteness, namely cyclic
subgroup separability and weak potency in various generalized free products and HNN
extensions. Among our results, we shall show that the generalized free products and HNN
extensions where the amalgamated or associated subgroups are finite, or central, or infinite
cyclic, or they are direct products of an infinite cyclic subgroup with a finite subgroup,
or they are finite extensions of central subgroups, are again cyclic subgroup separable or
weakly potent respectively. In order to prove our results, we shall prove a criterion each
for the weak potency of generalized free products and HNN extensions, but we shall use
previously established criterions for cyclic subgroup separability. Finally, we shall extend
our results to tree products and fundamental groups of graphs of groups.
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